Задачи Дирихле и Пуанкаре в многомерной области для одного класса сингулярных гиперболических уравнений
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Ключевые слова:
разрешимость задач, многомерная область, сингулярные уравнения, система уравненийАннотация
На плоскости было показано, что одна из фундаментальных задач математической физики - изучение колеблющейся струны некорректна, когда краевые условия заданы на всей границе области. Как доказано далее, задачи Дирихле некорректна не только для волнового уравнения, но и для общих гиперболических уравнений. В работах автора изучены задачи Дирихле и Пуанкаре для линейных многомерных гиперболических уравнений, где показаны корректность этих задач, существенна зависять от высоты рассматриваемой цилиндрической области. В данной работе найден многомерный область в которой, задачи Дирихле и Пуанкаре разрешимы для одного класса сингулярных гиперболических уравнений.
Библиографические ссылки
[1] J.Hadamard "Sur les problems aux derivees partielles et leur signification physique"// Princeton University Bulletin. -1902, -Vol.13, - P. 49-52.
[2] D.G.Bourgin and R.Duffin "The Dirichlet problem the vibrating string eguation"//Bulletin of the American Mathematical Society. -1939, -Vol.45, -P. 851-858.
[3] Shabat B. V Examples of solutions of the Dirichlet problem for a mixed-type equation // DAN SSSR. - 1957. - Vol. 112, No 3. - P. 386-389.
[4] Bitsadze A.B. The incorrectness of the Dirichlet problem for mixed-type equations in mixed areas // DAN USSR. - 1958. - Vol. 122, No 2. - P. 167-170.
[5] D.W.Fox and C.Pucci "The Dirichlet problem the wave eguation"// Annali di Mathematica Pura ed Applicata. -1958. - Vol. 46, -P. 155-182.
[6] Dunninger D.R., Zachmanoglou E.C. The condition for uniqueness of the Diriclet problem for hyperbolic equations in cilindrical domains // J.Math.Mech.-1969. Vol.18,-P.8.
[7] Nakhushev A. M. Displacement problems for partial differential equation. - М.: Nauka, 2006. - 287 p.
[8] Aldashev S.A. Aldashev S.A. Oh Dirichlet correctness task mnogomernix volnovogo equation and the equation Lavrenteva- Bicadze // Ukrainian . Matt . Zh .- 1996. - Vol. 4(48). No 5. - P.701-705.
[9] Aldashev S.A. The well - posedness of the Dirichlet problem in the cylindric domain for the multidimensional wave equation// Mathematical problems Engineering, volume 2010, Article ID 653215, 7 pages.
[10] Aldashev S.A. The well - posedness of the Poincare problem in a cylindrical domain for the higher-dimensional wave equation// Journal of Mathematical Science. -2011. - Vol. 173, No 2. -P. 150-154.
[11] Aldashev S.A. A uniqueness criterion for solutions of the Dirichlet problem and Poincare in a cylindrical domain for the multidimensional Euler-Poisson-Darboux // Far Mat. zhurn. - 2012. - Vol. 12, No 1. - P. 3-12.
[12] Aldashev S.A. Dirichlet and Poincare for a class of multidimensional singular hyperbolic equations // Scientific statements BSU, Ser. "Mathematics, Physics".- Belgorod, 2016. Vol. 43. No 13 (234), - P. 18-23.
[13] Mikhlin S.G. Multidimensijnal singular integrals and integral equations.-M.:Physmathgiz,1962.-254 p.
[14] Aldashev S.A. Boundary value problems for multidimensional hyperbolic and mixed equations. -Almaty: Gylym, 1994. -170 p.
[15] Copson E.T. On the Riemann-Green function // J.Rath.Mech and Anal. - 1958, No 1. - P. 324-348.
[16] Weinstein A. // The Fifth simposium in applied Math. MCGraw-Hill. New York. - 1954. - P.137-147.
[17] Nahushev A.M. Elements of fractional calculus and their application. -Nalchik: KBSC RAS, 2000,-298 p.
[18] Tersenov S.A. Introduction to the theory of equations degenerating on the boundary.- Novosibirsk: NSU, 1973, - 144 p.
[19] Aldashev S.A. Some boundary value problems for a class of singular partial differential equations derivatives // Differents.uravneniya. -1976. -Vol.12, No6.- P. 3-14.
[20] Tersenov S.A. Introduction to the theory of parabolic equations with changing time direction. -Novosibirsk: Siberian Branch of the USSR MI, 1982, -167 p.
[21] Aldashev S.A. Degenerate multidimensional hyperbolic equations. -Oral: ZKATU, 2007, -139 p.
[22] Aldashev S.A. Correctness of Dirichlet and Poincare problems in a multidimensional area for wave equalization // Ukrainian math journal. -2014. - Vol. 66, No 10. - P. 1414-1419.
[23] Kolmogorov A. N., Fomin S. V. Elements of function theory and functional analysis. –M.: Nauka, 1976. - 543 p.
[24] G.Beitmen, A.Erdeyee Higher Transcendental Functions. -M.: Nauka, 1973. - Vol. 1. - 294 p.
[2] D.G.Bourgin and R.Duffin "The Dirichlet problem the vibrating string eguation"//Bulletin of the American Mathematical Society. -1939, -Vol.45, -P. 851-858.
[3] Shabat B. V Examples of solutions of the Dirichlet problem for a mixed-type equation // DAN SSSR. - 1957. - Vol. 112, No 3. - P. 386-389.
[4] Bitsadze A.B. The incorrectness of the Dirichlet problem for mixed-type equations in mixed areas // DAN USSR. - 1958. - Vol. 122, No 2. - P. 167-170.
[5] D.W.Fox and C.Pucci "The Dirichlet problem the wave eguation"// Annali di Mathematica Pura ed Applicata. -1958. - Vol. 46, -P. 155-182.
[6] Dunninger D.R., Zachmanoglou E.C. The condition for uniqueness of the Diriclet problem for hyperbolic equations in cilindrical domains // J.Math.Mech.-1969. Vol.18,-P.8.
[7] Nakhushev A. M. Displacement problems for partial differential equation. - М.: Nauka, 2006. - 287 p.
[8] Aldashev S.A. Aldashev S.A. Oh Dirichlet correctness task mnogomernix volnovogo equation and the equation Lavrenteva- Bicadze // Ukrainian . Matt . Zh .- 1996. - Vol. 4(48). No 5. - P.701-705.
[9] Aldashev S.A. The well - posedness of the Dirichlet problem in the cylindric domain for the multidimensional wave equation// Mathematical problems Engineering, volume 2010, Article ID 653215, 7 pages.
[10] Aldashev S.A. The well - posedness of the Poincare problem in a cylindrical domain for the higher-dimensional wave equation// Journal of Mathematical Science. -2011. - Vol. 173, No 2. -P. 150-154.
[11] Aldashev S.A. A uniqueness criterion for solutions of the Dirichlet problem and Poincare in a cylindrical domain for the multidimensional Euler-Poisson-Darboux // Far Mat. zhurn. - 2012. - Vol. 12, No 1. - P. 3-12.
[12] Aldashev S.A. Dirichlet and Poincare for a class of multidimensional singular hyperbolic equations // Scientific statements BSU, Ser. "Mathematics, Physics".- Belgorod, 2016. Vol. 43. No 13 (234), - P. 18-23.
[13] Mikhlin S.G. Multidimensijnal singular integrals and integral equations.-M.:Physmathgiz,1962.-254 p.
[14] Aldashev S.A. Boundary value problems for multidimensional hyperbolic and mixed equations. -Almaty: Gylym, 1994. -170 p.
[15] Copson E.T. On the Riemann-Green function // J.Rath.Mech and Anal. - 1958, No 1. - P. 324-348.
[16] Weinstein A. // The Fifth simposium in applied Math. MCGraw-Hill. New York. - 1954. - P.137-147.
[17] Nahushev A.M. Elements of fractional calculus and their application. -Nalchik: KBSC RAS, 2000,-298 p.
[18] Tersenov S.A. Introduction to the theory of equations degenerating on the boundary.- Novosibirsk: NSU, 1973, - 144 p.
[19] Aldashev S.A. Some boundary value problems for a class of singular partial differential equations derivatives // Differents.uravneniya. -1976. -Vol.12, No6.- P. 3-14.
[20] Tersenov S.A. Introduction to the theory of parabolic equations with changing time direction. -Novosibirsk: Siberian Branch of the USSR MI, 1982, -167 p.
[21] Aldashev S.A. Degenerate multidimensional hyperbolic equations. -Oral: ZKATU, 2007, -139 p.
[22] Aldashev S.A. Correctness of Dirichlet and Poincare problems in a multidimensional area for wave equalization // Ukrainian math journal. -2014. - Vol. 66, No 10. - P. 1414-1419.
[23] Kolmogorov A. N., Fomin S. V. Elements of function theory and functional analysis. –M.: Nauka, 1976. - 543 p.
[24] G.Beitmen, A.Erdeyee Higher Transcendental Functions. -M.: Nauka, 1973. - Vol. 1. - 294 p.
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Как цитировать
Aldashev, S. A. (2018). Задачи Дирихле и Пуанкаре в многомерной области для одного класса сингулярных гиперболических уравнений. Вестник КазНУ. Серия математика, механика, информатика, 92(4), 20–31. извлечено от https://bm.kaznu.kz/index.php/kaznu/article/view/450
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